Subgroups — #35418331

Order 21248.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24917949	C₂	1	1	yes	maximal, characteristic
2	#24916379	C₂	1	1	yes	maximal, characteristic, complemented
3	#24916314	C₂	1	1	yes	maximal, characteristic, complemented
4	#24908371	C₂	1	1	yes	maximal, characteristic, complemented
5	#24908359	C₂	1	1	yes	maximal, characteristic, complemented
6	#24907994	C₂	1	2	yes	maximal, complemented
7	#24907989	C₂	1	2	yes	maximal, complemented
8	#24907949	C₂	1	2	yes	maximal, complemented
9	#24907942	C₂	1	2	yes	maximal, complemented
10	#24907218	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14581820	C₂²	1	2	yes	—
13	C₂×#14581814	C₂²	1	1	yes	characteristic
14	C₂²×D₆₆₄	C₂²	1	1	yes	characteristic
15	#19128467	C₂²	1	2	yes	—
16	#19128270	C₂²	1	2	yes	—
17	#19128175	C₂²	1	2	yes	—
18	#19128090	C₄	1	4	yes	complemented
19	#19128085	C₄	1	2	yes	complemented
20	#19128078	C₄	1	2	yes	complemented
21	#19127822	—	2	2	no	—
22	#19127817	—	2	2	no	—
23	#19127812	—	2	2	no	—
24	#19127783	—	2	2	no	—
25	#19127719	C₂²	1	2	yes	—
26	#19127717	C₂²	1	2	yes	—
27	#19127707	C₂²	1	2	yes	—
28	#19127705	C₂²	1	2	yes	—
29	C₂×#14581708	C₂²	1	2	yes	—
30	#19127674	C₂²	1	2	yes	—
31	#19127656	C₂²	1	1	yes	characteristic
32	#19127656	C₂²	1	1	yes	characteristic
33	C₈₃⋊#338	C₂²	1	1	yes	characteristic
34	#19127458	C₂²	1	1	yes	characteristic
35	#19127457	C₂²	1	1	yes	characteristic
36	#19127457	C₂²	1	1	yes	characteristic
37	C₂×#108×C₈₃	C₂²	1	1	yes	characteristic
38	#427×C₈₃	C₂²	1	1	yes	characteristic
39	#405×C₈₃	C₂²	1	1	yes	characteristic
40	#344×C₈₃	C₂²	1	2	yes	—
41	H(3,ℤ/4)×C₈₃	C₂²	1	2	yes	—
42	C₂×#13050590	C₂³	1	2	yes	—
43	C₂²×D₃₃₂	C₂³	1	2	yes	—
44	#14581820	—	4	2	no	—
45	#14581820	—	4	2	no	—
46	#14581814	—	2	1	no	—
47	#14581814	—	2	1	no	—
48	#14581814	—	2	1	no	—
49	#14581814	—	2	1	no	—
50	C₂×Dic₃₃₂	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×#13050579	C₂×C₄	1	2	yes	complemented
52	C₂×#13050579	C₂×C₄	1	4	yes	complemented
53	C₂×D₆₆₄	—	2	1	no	—
54	C₂×D₆₆₄	—	2	1	no	—
55	C₂×D₆₆₄	—	2	1	no	—
56	C₂×D₆₆₄	—	2	1	no	—
57	C₂×D₆₆₄	C₂×C₄	1	2	yes	—
58	C₂×D₆₆₄	C₂×C₄	1	2	yes	—
59	C₂×D₆₆₄	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×D₆₆₄	C₂×C₄	1	4	yes	complemented
61	#14581800	—	2	4	no	—
62	#14581798	—	4	2	no	—
63	C₂×#13050574	C₂³	1	1	yes	characteristic
64	C₂×#13050574	C₂³	1	1	yes	characteristic
65	M₁₆×D₈₃	—	4	2	no	—
66	#14581789	C₂×C₄	1	4	yes	complemented
67	#14581780	C₂×C₄	1	4	yes	complemented
68	#14581767	—	4	2	no	—
69	#14581762	—	4	2	no	—
70	C₄×D₃₃₂	—	4	2	no	—
71	#14581754	—	2	4	no	—
72	#14581751	C₂³	1	1	yes	characteristic
73	#14581751	C₂³	1	1	yes	characteristic
74	C₂²⋊C₄×D₈₃	—	4	2	no	—
75	#14581720	—	4	2	no	—
76	#14581718	—	2	4	no	—
77	#14581714	—	4	2	no	—
78	#14581712	—	2	4	no	—
79	#14581708	—	4	2	no	—
80	#14581706	—	4	2	no	—
81	#14581702	—	2	1	no	—
82	#14581702	D₄	1	2	yes	complemented
83	C₈×Dic₈₃	—	2	1	no	—
84	C₈×Dic₈₃	D₄	1	2	yes	complemented
85	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
86	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
88	#117×C₈₃	C₂³	1	2	yes	—
89	#117×C₈₃	C₂³	1	1	yes	characteristic
90	#108×C₈₃	—	2	1	no	—
91	#108×C₈₃	—	2	1	no	—
92	#107×C₈₃	—	2	1	no	—
93	#106×C₈₃	—	2	1	no	—
94	#97×C₈₃	C₂×C₄	1	2	yes	complemented
95	C₄×C₈×C₈₃	C₂×C₄	1	2	yes	complemented
96	C₂³×D₈₃	—	2	2	no	—
97	#13050590	—	2	2	no	—
98	#13050590	—	2	2	no	—
99	#13050590	—	2	2	no	—
100	#13050590	—	2	2	no	—
101	C₂×Dic₁₆₆	C₂²×C₄	1	2	yes	—
102	C₂×D₃₃₂	—	2	2	no	—
103	C₂×D₃₃₂	—	2	2	no	—
104	C₂×D₃₃₂	—	2	2	no	—
105	C₂×D₃₃₂	—	2	2	no	—
106	C₂×D₃₃₂	—	2	2	no	—
107	C₂×D₃₃₂	—	4	4	no	—
108	C₂×D₃₃₂	C₂²×C₄	1	4	yes	—
109	C₂×D₃₃₂	C₂²×C₄	1	2	yes	—
110	C₂×C₂²⋊D₈₃	—	2	2	no	—
111	C₂×C₄×D₈₃	—	2	2	no	—
112	C₂×C₄×D₈₃	—	4	4	no	—
113	Dic₃₃₂	—	2	1	no	—
114	Dic₃₃₂	—	2	1	no	—
115	#13050579	—	2	2	no	—
116	#13050579	—	2	2	no	—
117	#13050579	—	4	4	no	—
118	D₆₆₄	—	2	2	no	—
119	D₆₆₄	—	2	2	no	—
120	D₆₆₄	—	2	2	no	—
121	D₆₆₄	—	2	2	no	—
122	D₆₆₄	—	2	1	no	—
123	D₆₆₄	—	2	1	no	—
124	D₆₆₄	—	4	4	no	—
125	#13050574	—	2	1	no	—
126	#13050574	—	2	1	no	—
127	#13050574	—	2	1	no	—
128	#13050574	—	2	1	no	—
129	#13050573	—	4	4	no	—
130	C₂×C₈₃⋊C₈	—	2	1	no	—
131	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
132	C₈×D₈₃	—	4	4	no	—
133	C₄⋊Dic₈₃	—	2	1	no	—
134	C₄⋊Dic₈₃	—	2	1	no	—
135	C₂²⋊Dic₈₃	—	2	1	no	—
136	C₂²⋊Dic₈₃	—	2	1	no	—
137	(C₂×D₈₃)⋊C₄	—	4	4	no	—
138	(C₂×D₈₃)⋊C₄	—	4	4	no	—
139	C₄×Dic₈₃	—	2	1	no	—
140	C₄×Dic₈₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
142	M₁₆×C₈₃	—	2	1	no	—
143	M₁₆×C₈₃	—	2	1	no	—
144	M₁₆×C₈₃	—	2	2	no	—
145	M₁₆×C₈₃	—	2	2	no	—
146	C₂×C₈×C₈₃	—	2	2	no	—
147	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
153	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
154	C₄⋊C₄×C₈₃	—	2	1	no	—
155	C₄⋊C₄×C₈₃	—	2	2	no	—
156	C₂²⋊C₄×C₈₃	—	2	1	no	—
157	C₂²⋊C₄×C₈₃	—	2	2	no	—
158	C₄²×C₈₃	—	2	2	no	—
159	C₄²×C₈₃	C₂²×C₄	1	2	yes	—
160	C₂³×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₈₃	—	2	4	no	—
162	C₂²×D₈₃	—	2	2	no	—
163	C₂²×D₈₃	—	4	2	no	—
164	C₂²×D₈₃	—	4	2	no	—
165	C₂²×D₈₃	—	16	2	no	—
166	C₂×C₄×C₈₃	—	2	2	no	—
167	C₂×C₄×C₈₃	—	4	2	no	—
168	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂²⋊D₈₃	—	4	2	no	—
175	C₂²⋊D₈₃	—	4	2	no	—
176	C₂×Dic₈₃	—	2	2	no	—
177	C₂×Dic₈₃	—	2	2	no	—
178	C₂×Dic₈₃	—	4	1	no	—
179	D₃₃₂	—	2	4	no	—
180	D₃₃₂	—	2	2	no	—
181	D₃₃₂	—	2	2	no	—
182	D₃₃₂	—	2	4	no	—
183	D₃₃₂	—	4	2	no	—
184	D₃₃₂	—	4	2	no	—
185	D₃₃₂	—	16	4	no	—
186	C₄×D₈₃	—	4	2	no	—
187	C₄×D₈₃	—	4	2	no	—
188	C₄×D₈₃	—	16	4	no	—
189	Dic₁₆₆	—	2	2	no	—
190	Dic₁₆₆	—	2	2	no	—
191	C₈×C₈₃	—	2	2	no	—
192	C₈×C₈₃	—	4	2	no	—
193	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
194	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
195	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
196	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
197	C₈₃⋊C₈	—	2	2	no	—
198	C₈₃⋊C₈	—	4	1	no	—
199	C₂²×C₈₃	—	4	1	no	—
200	C₂²×C₈₃	#518	1	1	yes	characteristic
201	C₂²×C₈₃	#535	1	1	yes	characteristic
202	C₂²×C₈₃	#540	1	1	yes	characteristic
203	C₂×D₈₃	—	4	2	no	—
204	C₂×D₈₃	—	4	4	no	—
205	C₂×D₈₃	—	8	4	no	—
206	C₂×D₈₃	—	8	2	no	—
207	C₂×D₈₃	—	8	4	no	—
208	C₂×D₈₃	—	16	2	no	—
209	C₄×C₈₃	—	4	2	no	—
210	C₄×C₈₃	—	8	2	no	—
211	C₄×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
212	C₄×C₈₃	#518	1	1	yes	characteristic
213	C₄×C₈₃	#535	1	1	yes	characteristic
214	C₄×C₈₃	#540	1	1	yes	characteristic
215	Dic₈₃	—	4	2	no	—
216	Dic₈₃	—	4	2	no	—
217	Dic₈₃	—	8	1	no	—
218	#22286	—	83	1	no	maximal, Sylow
219	C₂×C₈₃	—	2	1	no	—
220	C₂×C₈₃	—	2	1	no	—
221	C₂×C₈₃	—	2	1	no	—
222	C₂×C₈₃	#2328	1	1	yes	characteristic
223	D₈₃	—	8	2	no	—
224	D₈₃	—	8	4	no	—
225	#3155	—	83	1	no	—
226	#2957	—	83	1	no	—
227	#2948	—	83	1	no	—
228	#1978	—	83	1	no	—
229	#1976	—	83	1	no	—
230	#1911	—	83	2	no	—
231	#1910	—	83	2	no	—
232	#1904	—	83	2	no	—
233	#1903	—	83	2	no	—
234	#1833	D₈₃	1	1	yes	characteristic, complemented
235	#1747	—	83	1	no	—
236	C₈₃	#22286	1	1	yes	characteristic, complemented, Sylow
237	C₂×AGL(1,ℤ/8)	—	83	2	no	—
238	C₂×#135	—	83	1	no	—
239	C₂²×D₈	—	83	1	no	—
240	#568	—	83	2	no	—
241	#535	—	83	2	no	—
242	#518	—	83	2	no	—
243	#496	—	83	4	no	—
244	#495	—	83	2	no	—
245	#493	—	83	2	no	—
246	#444	—	166	2	no	—
247	#443	—	166	2	no	—
248	#442	—	166	2	no	—
249	C₄×D₈	—	166	2	no	—
250	C₂×#108	C₂×D₈₃	1	1	yes	characteristic
251	#427	C₂×D₈₃	1	1	yes	characteristic
252	#421	—	83	2	no	—
253	#421	—	83	2	no	—
254	#418	—	83	2	no	—
255	#418	—	83	2	no	—
256	C₂×#100	—	83	2	no	—
257	#410	—	83	2	no	—
258	#405	—	83	1	no	—
259	#405	—	83	1	no	—
260	#405	C₂×D₈₃	1	1	yes	characteristic
261	#344	C₂×D₈₃	1	2	yes	—
262	#338	—	83	1	no	—
263	H(3,ℤ/4)	—	83	1	no	—
264	H(3,ℤ/4)	—	83	1	no	—
265	H(3,ℤ/4)	—	83	1	no	—
266	H(3,ℤ/4)	C₂×D₈₃	1	2	yes	—
267	C₂×#41	—	83	2	no	—
268	C₂²×D₄	—	83	2	no	—
269	AGL(1,ℤ/8)	—	332	2	no	—
270	AGL(1,ℤ/8)	—	332	2	no	—
271	#135	—	166	1	no	—
272	#135	—	166	1	no	—
273	#135	—	166	1	no	—
274	#135	—	166	1	no	—
275	C₂×Q₁₆	—	83	1	no	—
276	C₂×SD₁₆	—	83	4	no	—
277	C₂×SD₁₆	—	83	2	no	—
278	C₂×D₈	—	83	4	no	—
279	C₂×D₈	—	83	2	no	—
280	C₂×D₈	—	83	2	no	—
281	C₂×D₈	—	83	1	no	—
282	C₂×D₈	—	166	1	no	—
283	C₂×D₈	—	166	1	no	—
284	C₂×D₈	—	166	1	no	—
285	C₂×D₈	—	166	1	no	—
286	#131	—	332	2	no	—
287	#131	—	166	4	no	—
288	C₂×M₁₆	—	332	2	no	—
289	C₂×M₁₆	—	83	1	no	—
290	C₂×M₁₆	—	83	1	no	—
291	C₂×M₁₆	C₂²×D₈₃	1	2	yes	—
292	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
294	#127	—	83	4	no	—
295	#124	—	83	4	no	—
296	#121	—	332	2	no	—
297	#120	—	332	2	no	—
298	C₄×D₄	—	332	2	no	—
299	C₄×D₄	—	166	4	no	—
300	#117	—	83	1	no	—
301	#117	—	83	1	no	—
302	#117	C₂²×D₈₃	1	2	yes	—
303	#117	C₂²×D₈₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	332	2	no	—
305	#108	—	2	1	no	—
306	#108	—	2	1	no	—
307	#107	—	2	1	no	—
308	#106	—	2	1	no	—
309	#104	—	332	2	no	—
310	#104	—	166	4	no	—
311	#102	—	332	2	no	—
312	#102	—	166	4	no	—
313	#100	—	332	2	no	—
314	#99	—	332	2	no	—
315	#97	—	83	2	no	—
316	#97	—	166	1	no	—
317	#97	C₄×D₈₃	1	2	yes	complemented
318	C₄×C₈	—	83	2	no	—
319	C₄×C₈	—	166	1	no	—
320	C₄×C₈	C₄×D₈₃	1	2	yes	complemented
321	C₂⁴	—	166	2	no	—
322	#41	—	166	2	no	—
323	#41	—	166	2	no	—
324	#41	—	166	2	no	—
325	#41	—	166	2	no	—
326	C₂×Q₈	—	83	2	no	—
327	C₂×D₄	—	332	4	no	—
328	C₂×D₄	—	83	4	no	—
329	C₂×D₄	—	83	2	no	—
330	C₂×D₄	—	166	2	no	—
331	C₂×D₄	—	166	2	no	—
332	C₂×D₄	—	166	2	no	—
333	C₂×D₄	—	166	2	no	—
334	C₂×D₄	—	166	2	no	—
335	C₂×D₄	—	166	2	no	—
336	C₂²×C₄	—	332	4	no	—
337	C₂²×C₄	—	166	2	no	—
338	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
339	Q₁₆	—	166	1	no	—
340	Q₁₆	—	166	1	no	—
341	SD₁₆	—	332	4	no	—
342	SD₁₆	—	166	2	no	—
343	SD₁₆	—	166	2	no	—
344	D₈	—	332	4	no	—
345	D₈	—	166	2	no	—
346	D₈	—	166	2	no	—
347	D₈	—	166	2	no	—
348	D₈	—	166	2	no	—
349	D₈	—	166	1	no	—
350	D₈	—	166	1	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	332	4	no	—
356	M₁₆	—	166	1	no	—
357	M₁₆	—	166	1	no	—
358	M₁₆	—	166	1	no	—
359	M₁₆	—	166	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	332	4	no	—
362	C₂×C₈	—	83	2	no	—
363	C₂×C₈	—	166	1	no	—
364	C₂×C₈	C₂×C₄×D₈₃	1	2	yes	—
365	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
367	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
368	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
369	C₂×C₈	#13050591	1	1	yes	characteristic
370	C₂×C₈	#13050591	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	166	1	no	—
374	C₄⋊C₄	—	166	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	332	4	no	—
378	C₂²⋊C₄	—	332	4	no	—
379	C₂²⋊C₄	—	166	1	no	—
380	C₂²⋊C₄	—	166	1	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	83	2	no	—
383	C₄²	—	166	1	no	—
384	C₄²	C₂×C₄×D₈₃	1	2	yes	—
385	C₂³	—	1328	2	no	—
386	C₂³	—	332	2	no	—
387	C₂³	—	332	2	no	—
388	C₂³	—	166	4	no	—
389	C₂³	—	166	2	no	—
390	C₂³	#14581838	1	1	yes	characteristic
391	Q₈	—	166	2	no	—
392	Q₈	—	166	2	no	—
393	D₄	—	1328	4	no	—
394	D₄	—	332	2	no	—
395	D₄	—	332	2	no	—
396	D₄	—	332	2	no	—
397	D₄	—	332	2	no	—
398	D₄	—	166	4	no	—
399	D₄	—	166	2	no	—
400	D₄	—	166	2	no	—
401	D₄	—	166	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	1328	4	no	—
405	C₂×C₄	—	332	2	no	—
406	C₂×C₄	—	332	2	no	—
407	C₂×C₄	—	332	1	no	—
408	C₂×C₄	—	166	2	no	—
409	C₂×C₄	—	166	2	no	—
410	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
411	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
412	C₂×C₄	C₂×#13050591	1	1	yes	characteristic
413	C₂×C₄	#14581838	1	1	yes	characteristic
414	C₂×C₄	#14581838	1	1	yes	characteristic
415	C₂×C₄	#14581838	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	332	1	no	—
419	C₈	—	166	2	no	—
420	C₈	#14581754	1	1	yes	characteristic
421	C₈	#14581754	1	1	yes	characteristic
422	C₈	#14581754	1	1	yes	characteristic
423	C₈	#14581754	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	1328	2	no	—
426	C₂²	—	332	2	no	—
427	C₂²	—	332	4	no	—
428	C₂²	—	664	2	no	—
429	C₂²	—	664	4	no	—
430	C₂²	—	664	4	no	—
431	C₂²	#19128175	1	1	yes	characteristic
432	C₂²	#19128269	1	1	yes	characteristic
433	C₂²	#19128307	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	8	2	no	—
436	C₄	—	332	2	no	—
437	C₄	—	332	2	no	—
438	C₄	—	664	1	no	—
439	C₄	C₂×#14581754	1	1	yes	characteristic
440	C₄	#19128175	1	1	yes	characteristic
441	C₄	#19128269	1	1	yes	characteristic
442	C₄	#19128307	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	664	4	no	—
447	C₂	—	664	2	no	—
448	C₂	#24910186	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#24910186
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₈₃×#1833	C₂
socle	C₂×C₈₃	#2328
prime radical	#24917949	C₂
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	#1833	D₈₃
hypocenter	C₈₃	#22286
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1833

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #24916379	C₂	semidirect
3. #24916314	C₂	semidirect
4. #24908371	C₂	semidirect
5. #24908359	C₂	semidirect
6. #24907994	C₂	semidirect
7. #24907989	C₂	semidirect
8. #24907949	C₂	semidirect
9. #24907942	C₂	semidirect
10. #24907218	C₂	semidirect
11. C₈₃×#1833	C₂	semidirect
18. #19128090	C₄	semidirect
19. #19128085	C₄	semidirect
20. #19128078	C₄	semidirect
50. C₂×Dic₃₃₂	C₂×C₄	semidirect
51. C₂×#13050579	C₂×C₄	semidirect
52. C₂×#13050579	C₂×C₄	semidirect
59. C₂×D₆₆₄	C₂×C₄	semidirect
60. C₂×D₆₆₄	C₂×C₄	semidirect
66. #14581789	C₂×C₄	semidirect
67. #14581780	C₂×C₄	semidirect
82. #14581702	D₄	semidirect
84. C₈×Dic₈₃	D₄	semidirect
94. #97×C₈₃	C₂×C₄	semidirect
95. C₄×C₈×C₈₃	C₂×C₄	semidirect
234. #1833	D₈₃	semidirect
236. C₈₃	#22286	semidirect
317. #97	C₄×D₈₃	semidirect
320. C₄×C₈	C₄×D₈₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#24917949	2
#24916379	2
#24916314	2
#24908371	2
#24908359	2
#24907994	2
#24907989	2
#24907949	2
#24907942	2
#24907218	2
C₈₃×#1833	2
#22286	83